Sigma models as Gross-Neveu models

TL;DR

This paper explores the deep mathematical and physical connections between integrable sigma models and Gross-Neveu models, highlighting their geometric structures, deformations, and extensions with fermions.

Contribution

It provides a comprehensive review of the correspondence between sigma models and Gross-Neveu models, including their geometric aspects and various deformations.

Findings

Establishes a detailed correspondence between sigma and Gross-Neveu models.

Analyzes geometric structures and phase spaces of the models.

Discusses deformations, Ricci flow, and fermionic extensions.

Abstract

We review the correspondence between integrable sigma models with complex homogeneous target spaces and chiral bosonic (and possibly mixed bosonic/fermionic) Gross-Neveu models. Mathematically, the latter are models with quiver variety phase spaces, which reduce to the more conventional sigma models in special cases. We discuss the geometry of the models, as well as their trigonometric and elliptic deformations, Ricci flow and the inclusion of fermions.